The answer is: Yes, it is a function. The function is linear.
The explanation is shown below:
1. You must keep on mind the following information:
is a function when for each value of the domain
there is an unique value of
. For example:

2. A linear function has the following form:

Where
is the slope and
is the y-intercept.
3. When the slope is zero, you have that
. Therefore:

4. As you can see, it is a linear function with
.